Towards a holistic sulfate-water-O2 triple oxygen isotope systematics

Triple oxygen isotope (∆¹⁷O with δ¹⁸O) signals of H₂O and O₂ found in sulfate of oxidative weathering origin offer promising constraints on modern and ancient weathering, hydrology, atmospheric gas concentrations, and bioproductivity. However, interpretations of the sulfate-water-O₂ system rely on assuming fixed oxygen-isotope fractionations between sulfate and water, which, contrastingly, are shown to vary widely in sign and amplitude. Instead, here we anchor sulfate-water-O₂ triple oxygen isotope systematics on the homogeneous composition of atmospheric O₂ with empirical constraints and modeling. Our resulting framework does not require a priori assumptions of the O₂- versus H₂O‑oxygen ratio in sulfate and accounts for the signals of mass-dependent and mass-independent fractionation in the ∆¹⁷O and δ¹⁸O of sulfate's O₂‑oxygen source. Within this framework, new ∆¹⁷O measurements of sulfate constrain ~2.3 Ga Paleoproterozoic gross primary productivity to between 6 and 160 times present-day levels, with important implications for the biological carbon cycle response to high CO₂ concentrations prevalent on the early Earth.